标准神经网络模型及其应用

Standard neural network model and its application

提出一种新的神经网络模型——标准神经网络模型(SNNM),它由线性动力学系统和有界静态非线性算子连接而成.SNNM表示为线性微分包含(LDI)形式,可以方便地利用线性矩阵不等式(LMI)方法来分析其稳定性和其他性能.利用不同的Lyapunov函数和S方法推导出基于LMI的连续SNNM和离散SNNM的稳定性定理.实例表明SNNM可应用于递归神经网络的稳定性分析以及神经网络控制系统的综合和分析.

The novel neural network model, named standard neural network model (SNNM), is the interconnection of a linear dynamic system and a bounded static nonlinear operator. The SNNM is represented by linear differential inclusion (LDI), which allows taking advantage of the linear matrix inequality (LMI) approach in the stability analysis or other performance analysis of SNNM. By combining a number of different Lyapunov functions with S-procedure, some useful stability theorems for continuous SNNM and discrete-time SNNM were derived, whose conditions were formulated as LMIs. Some examples show that the proposed SNNM can be applied in analyzing the stability of recurrent neural network, and synthesizing the neural network control system.